Model of convective heat exchange due to isolated thermals in the atmospheric boundary layer

Abstract

A numerical model of convective heat transfer due to isolated thermals in the atmospheric boundary layer is used to describe the temperature profile transformation in undisturbed conditions as a result of intensive dry free convection. Based on some assumptions, the heat transfer Equation (2) is transformed to the form (14) in which the coefficients and the function F are expressed by (d/dz)(ln ϱ) and by parameters of thermals. Equation (14) has been solved numerically with the help of Equation (15) obtained from the statics equation because of Equation (8). The size distribution function f(z, r, t) of the thermals is discrete (Table I), according to Vulf'son (1961). On Figures 1 and 2 are plotted successive temperature profiles for a ground inversion, transformed due to free convection and turbulence (Figures 1a and 2a), and due to turbulence only (Figures 1b and 2b). The profiles are computed from Equation 14 (Figures 1a and 2a) and Equation 16 (Figures 1b and 2b) for k _z= 1 m² s⁻¹ (Figure 1) and k _z= 10 m² s⁻¹ (Figure 2). On Figure 3 the real temperature profiles in Sofia for June 22nd 1976 are compared with the profiles computed using the real initial profile for 4.30 h local time. Good qualitative agreement can be seen.